Standard #: MAFS.912.G-C.1.2 (Archived Standard)


This document was generated on CPALMS - www.cpalms.org



Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.


General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Circles
Cluster: Understand and apply theorems about circles. (Geometry - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :
    Items may include finding or describing the length of arcs when given
    information. 
    Calculator :

    Neutral

    Clarification :
    Students will solve problems related to circles using the properties of
    central angles, inscribed angles, circumscribed angles, diameters,
    radii, chords, and tangents. 
    Stimulus Attributes :
    Items may be set in a real-world or mathematical context. 
    Response Attributes :
    Items may require the student to use or choose the correct unit of
    measure. 


Sample Test Items (1)

Test Item # Question Difficulty Type
Sample Item 1

In the diagram shown, chords AB and CD intersect at E. The measure of begin mathsize 12px style stack A C with overparenthesis on top end style is 120º, the measure of begin mathsize 12px style stack D B with overparenthesis on top end style is (2x)º, and the measure of begin mathsize 12px style angle A E C end style is (4x)º.

What is the degree measure of begin mathsize 12px style angle A E D end style?

N/A EE: Equation Editor


Related Courses

Course Number1111 Course Title222
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))


Related Resources

Educational Game

Name Description
Tangled Web: An Angle Relationships Game

You are a robotic spider tangled up in an angular web. Use your knowledge of angle relationships to collect flies and teleport through wormholes to rescue your spider family!

Formative Assessments

Name Description
Central and Inscribed Angles

Students are asked to describe the relationship between a central angle and an inscribed angle that intercept the same arc.

Tangent Line and Radius

Students are asked to draw a circle, a tangent to the circle, and a radius to the point of tangency. Students are then asked to describe the relationship between the radius and the tangent line.

Inscribed Angle on Diameter

Students are asked to find the measures of two inscribed angles of a circle.

Circles with Angles

Students are given a diagram with inscribed, central, and circumscribed angles and are asked to identify each type of angle, determine angle measures, and describe relationships among them.

Lesson Plans

Name Description
The Seven Circles Water Fountain

This lesson provides an opportunity for students to apply concepts related to circles, angles, area, and circumference to a design situation. 

Geometry Problems: Circles and Triangles

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties:

  • Solving problems by determining the lengths of the sides in right triangles.
  • Finding the measurements of shapes by decomposing complex shapes into simpler ones.

The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

Inscribing and Circumscribing Right Triangles This lesson is designed to enable students to develop strategies for describing relationships between right triangles and the radii of their inscribed and circumscribed circles.
Seeking Circle Angles

Students will start this lesson with a win-lose-draw game to review circle vocabulary words. They will then use examples on a discovery sheet to discover the relationships between arcs and the angles whose vertex is located on a circle, in the interior of the circle, and exterior to the circle. They will wrap up the lesson in a class discussion and questions answered on white boards.

Seeking Circle Segments

Students will start this lesson with a "Pictionary" game to review circle vocabulary terms. They will then use computers and GeoGebra to discover the relationships between portions of segments that intersect in the interior of the circle, and exterior to the circle. They will wrap up the lesson in a class discussion and consensus on rules (formulas).

Problem-Solving Tasks

Name Description
Two Wheels and a Belt

This task combines two skills: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment, and computing lengths of circular arcs given the radii and central angles.

Right triangles inscribed in circles II

This problem solving task asks students to explain certain characteristics about a triangle.

Right triangles inscribed in circles I

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle: the fact that these triangles are always right triangles is often referred to as Thales' theorem.

Tangent Lines and the Radius of a Circle

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.

Neglecting the Curvature of the Earth

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

Student Resources

Problem-Solving Tasks

Name Description
Two Wheels and a Belt:

This task combines two skills: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment, and computing lengths of circular arcs given the radii and central angles.

Right triangles inscribed in circles II:

This problem solving task asks students to explain certain characteristics about a triangle.

Right triangles inscribed in circles I:

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle: the fact that these triangles are always right triangles is often referred to as Thales' theorem.

Tangent Lines and the Radius of a Circle:

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.

Neglecting the Curvature of the Earth:

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.



Parent Resources

Problem-Solving Tasks

Name Description
Two Wheels and a Belt:

This task combines two skills: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment, and computing lengths of circular arcs given the radii and central angles.

Right triangles inscribed in circles II:

This problem solving task asks students to explain certain characteristics about a triangle.

Right triangles inscribed in circles I:

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle: the fact that these triangles are always right triangles is often referred to as Thales' theorem.

Tangent Lines and the Radius of a Circle:

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.

Neglecting the Curvature of the Earth:

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.



Printed On:8/17/2022 1:58:32 PM
Print Page | Close this window